The continuous version of Weihrauch reducibility has always been studied alongside the computable
version, and all four reducibilities induce a lattice structure (see [1]} for references).
Normally, the Weihrauch lattice refers
to the lattice induced by \(\mathop {\le _{\mathrm {W}}}\) , but here we will freely use this term also for the lattice structure induced by \(\le _\mathrm {W}^*\) . If we want to be more precise, we will call the latter the continuous Weihrauch lattice.This should not be misunderstood such that the structure is continuous as a lattice, but it just indicates that we
refer to the lattice structure induced by the continuous version of the reducibility.
Even though this lattice has been studied for about 30 years, very little is known about the structure of the lattice closer
towards the bottom. Indeed Matthias Schröder has asked the following questionThe original question is phrased slightly differently, but we interpret it in the intended way. [2]}.
